$\begin{array}{l}
A = \frac{{x - y}}{{x + y}} = \frac{{(x - y)(x + y)}}{{{{(x + y)}^2}}} = \frac{{{x^2} - {y^2}}}{{{x^2} + 2xy + {y^2}}}\\
B = \frac{{{x^2} - {y^2}}}{{{x^2} + {y^2}}}\\
x < y < 0 \to 2xy > 0 \to {x^2} + 2xy + {y^2} > {x^2} + {y^2} > 0\\
x < y < 0 \to {x^2} - {y^2} < 0\\
\to A > B
\end{array}$